Caledonian: the difference is that if you know that the photon was sent out, you have infinite computing power, and you want to know the exact subjective probability distribution you should hold for what a particular brontosaur ate for lunch 123 million years ago, you need to take that photon into account. You can then test that by looking for the fossilized dung in exactly the right set of places and you will probably find the relevant dung faster than your competition who started without knowledge of the photon in question.